6. THE HUBBLE SEQUENCE IN THE HIERARCHICAL COSMOGONY

In the previous sections we have pointed out several processes which
intervene in the evolution of luminous galaxies. Summarizing, the first
step in galaxy formation is the assembling of the dark matter halos,
which may happen either quiescently or violently, depending mostly
on the environment. In the former case, the gas trapped inside the halos
dissipates (radiatively and turbulently), infalls to the center and forms an
inside-out disk in centrifugal equilibrium with a surface density that
depends mainly on the halo spin parameter. SF in disks is expected to be
stationary and self-regulated by feedback and turbulent dissipation. In
this case, the main drivers of the SF history are the gas infall and the
angular momentum.
Both of them are tightly related to the cosmological conditions. Some disks
may suffer further morphological evolution due to internal gravitational
instabilities (spiral arms, bars and bulges).

However, the strongest changes are expected when violent major mergers
occur: the stellar disk is heated and gas angular momentum is transferred,
leading to the formation of spheroids and SF bursts.
In this phase ULIGs and AGNs can appear. The products of galaxy collisions
depend on the gas fraction, the stellar disk-to-bulge ratio and the
dynamics of the encounter
(Barnes & Hernquist
1991,
1996;
Mihos & Hernquist
1994,
1996;
Barnes 2002).
Numerical simulations show that a wide range of final products can
be obtained, depending on these parameters. Nevertheless, the stellar
component is almost always heated and thickened, acquiring the structure
of a spheroid.
The gas that suffers strong shocks transfers its angular momentum, and may
originate a bulge. The gas that has not been involved in strong shocks
retains a large amount of angular momentum and can feed an extended disk.
Accretion from the environment supplies the spheroid/disk system with
further angular-momentum-rich gas.
The ultimate fate of gas is to be converted into stars.
When the gas surface density is sufficiently high, the disk stellar
population is practically coeval to the bulge, but as the gas surface
density is lower, the slower is the SF rate.

In the hierarchical framework, the major merging rate is easily
estimated by the
extended Press-Schechter formalism or by N-body simulations (e.g.,
Gottloeber et al. 2001)
and, for a given mass, is increasing with z.
Multiplying the merging rate by the halo mass function at different
z's, one obtains that the merging rate density (per unit of
volume) for halos with masses smaller than 1013
M has its
maximum at z > 1; for halos in clusters,
the maximum is shifted to earlier epochs. Therefore, most of spheroids,
upon the understanding that they arise from major mergers, are born at
high redshifts, when galaxies are still gas rich. The smaller fraction
of major mergers at late epochs occurs mainly between gas-poor galaxies
with an
important spheroidal component. Around the spheroid a disk grows by gas
accretion according to the conditions of the environment and by the energy
feedback of the spheroid, the bulge-to-disk mass ratio being an
indicator of the Hubble type. When the spheroid is more massive than the
disk, we have an elliptical or S0 galaxy. The lack of a massive disk in
these cases may be due to the facts that (i) the merger has
occurred recently, (ii) the gas accretion has been inhibited, or
(iii) the environment is poor
in gas. The existence of field elliptical galaxies with an old stellar
population may be indicative of conditions that inhibit the formation and
growth of a disk.

Using semi-analytic modelation and taking into account many of the physical
processes mentioned above,
Cole et al. (2000)
have made predictions
about the morphology mixing of galaxies and the dependence on
the environment. Their models reproduce the relative number of E+S0
galaxies. However, concerning the age of spheroids, the situation is
not so clear. Their predicted colour-magnitude relation for ellipticals in
clusters is significantly flatter than that observed at bright magnitudes.
Benson et al. (2002)
have compared the same models with samples of field
spheroidal galaxies with redshifts up to two. Models reveal some difficulty
predicting the observed red population of E+S0 galaxies, while on the blue
side the agreement is satisfactory. Colours reflect only
approximately the ages of old spheroids. The ages of
elliptical galaxies derived by different observational
methods, such as those mentioned in
section 5.1, are difficult to
reconcile with the model predictions. Again, the situation could be
alleviated if gas accretion and disk growth around
spheroids would be inhibited (item (ii) above), in this way allowing some
of the spheroids to evolve with a negligible SF activity.
A careful comparison between models and observations
of the relation between the intrinsic colours of the
disk and the Hubble type should be of some relevance.
In fact, a growing disk around a spheroid would evolve
inside-out from blue to red while the bulge-to-disk
ratio decreases; however, this situation depends on the
physical conditions created by the collision as well
by gas accretion and the intense feedback.

Back to galaxy collisions, it should be noted that its stochastic
nature (as well as the extended redshift range of spheroid formation)
contribute to the scatter of the FJR and KR, and possibly of the FP.
While the scatter of TFR is a faithful product of the stochastical
properties of the primordial density fluctuations
(Section 4.1), the scatters of the spheroid
scaling relations (FJR, KR, FP) are further increased by the astrophysical
processes in which they have been involved (collisions, feedback).